Let X1,...,XNbe draws from the random variable X

1. Prove that1/NSigma (XiXn)^2 is a consistent estimator forVar(X)

2. Prove that1/N Sigma (XiXn)^2 is not an unbiased estimator forVar(X)

3. Give a consistent and unbiased estimator forE(X^2)

4. Give a consistent estimator forE(X^2)Var(X)